arXiv subjects

Yin Yang

Publications and source records attributed to Yin Yang.

At least 91 records · Page 5Linked to original sources

arXiv2025

Fractional coupled Halanay inequality and its applications

This paper introduces a generalized fractional Halanay-type coupled inequality, which serves as a robust tool for characterizing the asymptotic stability of diverse time fractional functional differential equations, particularly those exhibiting Mittag-Leffler type stability. Our main tool is a sub-additive property of Mittag-Leffler function and its optimal asymptotic decay rate estimation. Our results further optimize and improve some existing results in the literature. We illustrate two significant applications of this fractional Halanay-type inequality. Firstly, by combining our results in this work with the positive representation method positive representation of delay differential systems, we establish an asymptotic stability criterion for a category of linear fractional coupled systems with bounded delays. This criterion extends beyond the traditional boundaries of positive system theory, offering a new perspective on stability analysis in this domain. Secondly, through energy estimation, we establish the contractility and dissipativity of a class of time fractional neutral functional differential equations. Our analysis reveals the typical long-term polynomial decay behavior inherent in time fractional evolutionary equations, thereby providing a solid theoretical foundation for subsequent numerical investigations.

math.NA↗

arXiv2025

3DGS$^2$: Near Second-order Converging 3D Gaussian Splatting

3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior efficiency. As a learning-based approach, 3DGS training has been dealt with the standard stochastic gradient descent (SGD) method, which offers at most linear convergence. Consequently, training often requires tens of minutes, even with GPU acceleration. This paper introduces a (near) second-order convergent training algorithm for 3DGS, leveraging its unique properties. Our approach is inspired by two key observations. First, the attributes of a Gaussian kernel contribute independently to the image-space loss, which endorses isolated and local optimization algorithms. We exploit this by splitting the optimization at the level of individual kernel attributes, analytically constructing small-size Newton systems for each parameter group, and efficiently solving these systems on GPU threads. This achieves Newton-like convergence per training image without relying on the global Hessian. Second, kernels exhibit sparse and structured coupling across input images. This property allows us to effectively utilize spatial information to mitigate overshoot during stochastic training. Our method converges an order faster than standard GPU-based 3DGS training, requiring over $10\times$ fewer iterations while maintaining or surpassing the quality of the compared with the SGD-based 3DGS reconstructions.

cs.CV↗

arXiv2024

PhysMotion: Physics-Grounded Dynamics From a Single Image

We introduce PhysMotion, a novel framework that leverages principled physics-based simulations to guide intermediate 3D representations generated from a single image and input conditions (e.g., applied force and torque), producing high-quality, physically plausible video generation. By utilizing continuum mechanics-based simulations as a prior knowledge, our approach addresses the limitations of traditional data-driven generative models and result in more consistent physically plausible motions. Our framework begins by reconstructing a feed-forward 3D Gaussian from a single image through geometry optimization. This representation is then time-stepped using a differentiable Material Point Method (MPM) with continuum mechanics-based elastoplasticity models, which provides a strong foundation for realistic dynamics, albeit at a coarse level of detail. To enhance the geometry, appearance and ensure spatiotemporal consistency, we refine the initial simulation using a text-to-image (T2I) diffusion model with cross-frame attention, resulting in a physically plausible video that retains intricate details comparable to the input image. We conduct comprehensive qualitative and quantitative evaluations to validate the efficacy of our method. Our project page is available at: https://supertan0204.github.io/physmotion_website/.

cs.CV↗

arXiv2024

MVMS-RCN: A Dual-Domain Unfolding CT Reconstruction with Multi-sparse-view and Multi-scale Refinement-correction

X-ray Computed Tomography (CT) is one of the most important diagnostic imaging techniques in clinical applications. Sparse-view CT imaging reduces the number of projection views to a lower radiation dose and alleviates the potential risk of radiation exposure. Most existing deep learning (DL) and deep unfolding sparse-view CT reconstruction methods: 1) do not fully use the projection data; 2) do not always link their architecture designs to a mathematical theory; 3) do not flexibly deal with multi-sparse-view reconstruction assignments. This paper aims to use mathematical ideas and design optimal DL imaging algorithms for sparse-view tomography reconstructions. We propose a novel dual-domain deep unfolding unified framework that offers a great deal of flexibility for multi-sparse-view CT reconstruction with different sampling views through a single model. This framework combines the theoretical advantages of model-based methods with the superior reconstruction performance of DL-based methods, resulting in the expected generalizability of DL. We propose a refinement module that utilizes unfolding projection domain to refine full-sparse-view projection errors, as well as an image domain correction module that distills multi-scale geometric error corrections to reconstruct sparse-view CT. This provides us with a new way to explore the potential of projection information and a new perspective on designing network architectures. All parameters of our proposed framework are learnable end to end, and our method possesses the potential to be applied to plug-and-play reconstruction. Extensive experiments demonstrate that our framework is superior to other existing state-of-the-art methods. Our source codes are available at https://github.com/fanxiaohong/MVMS-RCN.

eess.IV↗

arXiv2024

Atlas3D: Physically Constrained Self-Supporting Text-to-3D for Simulation and Fabrication

Existing diffusion-based text-to-3D generation methods primarily focus on producing visually realistic shapes and appearances, often neglecting the physical constraints necessary for downstream tasks. Generated models frequently fail to maintain balance when placed in physics-based simulations or 3D printed. This balance is crucial for satisfying user design intentions in interactive gaming, embodied AI, and robotics, where stable models are needed for reliable interaction. Additionally, stable models ensure that 3D-printed objects, such as figurines for home decoration, can stand on their own without requiring additional supports. To fill this gap, we introduce Atlas3D, an automatic and easy-to-implement method that enhances existing Score Distillation Sampling (SDS)-based text-to-3D tools. Atlas3D ensures the generation of self-supporting 3D models that adhere to physical laws of stability under gravity, contact, and friction. Our approach combines a novel differentiable simulation-based loss function with physically inspired regularization, serving as either a refinement or a post-processing module for existing frameworks. We verify Atlas3D's efficacy through extensive generation tasks and validate the resulting 3D models in both simulated and real-world environments.

cs.LG↗

arXiv2024

ARM: Appearance Reconstruction Model for Relightable 3D Generation

Recent image-to-3D reconstruction models have greatly advanced geometry generation, but they still struggle to faithfully generate realistic appearance. To address this, we introduce ARM, a novel method that reconstructs high-quality 3D meshes and realistic appearance from sparse-view images. The core of ARM lies in decoupling geometry from appearance, processing appearance within the UV texture space. Unlike previous methods, ARM improves texture quality by explicitly back-projecting measurements onto the texture map and processing them in a UV space module with a global receptive field. To resolve ambiguities between material and illumination in input images, ARM introduces a material prior that encodes semantic appearance information, enhancing the robustness of appearance decomposition. Trained on just 8 H100 GPUs, ARM outperforms existing methods both quantitatively and qualitatively.

cs.CV↗

arXiv2024

Efficient GPU Cloth Simulation with Non-distance Barriers and Subspace Reuse

This paper pushes the performance of cloth simulation, making the simulation interactive even for high-resolution garment models while keeping every triangle untangled. The penetration-free guarantee is inspired by the interior point method, which converts the inequality constraints to barrier potentials. We propose a major overhaul of this modality within the projective dynamics framework by leveraging an adaptive weighting mechanism inspired by barrier formulation. This approach does not depend on the distance between mesh primitives, but on the virtual life span of a collision event and thus keeps all the vertices within feasible region. Such a non-distance barrier model allows a new way to integrate collision resolution into the simulation pipeline. Another contributor to the performance boost comes from the subspace reuse strategy. This is based on the observation that low-frequency strain propagation is near orthogonal to the deformation induced by collisions or self-collisions, often of high frequency. Subspace reuse then takes care of low-frequency residuals, while high-frequency residuals can also be effectively smoothed by GPU-based iterative solvers. We show that our method outperforms existing fast cloth simulators by at least one order while producing high-quality animations of high-resolution models.

cs.GR↗

arXiv2024

Volumetric Homogenization for Knitwear Simulation

This paper presents volumetric homogenization, a spatially varying homogenization scheme for knitwear simulation. We are motivated by the observation that macro-scale fabric dynamics is strongly correlated with its underlying knitting patterns. Therefore, homogenization towards a single material is less effective when the knitting is complex and non-repetitive. Our method tackles this challenge by homogenizing the yarn-level material locally at volumetric elements. Assigning a virtual volume of a knitting structure enables us to model bending and twisting effects via a simple volume-preserving penalty and thus effectively alleviates the material nonlinearity. We employ an adjoint Gauss-Newton formulation to battle the dimensionality challenge of such per-element material optimization. This intuitive material model makes the forward simulation GPU-friendly. To this end, our pipeline also equips a novel domain-decomposed subspace solver crafted for GPU projective dynamics, which makes our simulator hundreds of times faster than the yarn-level simulator. Experiments validate the capability and effectiveness of volumetric homogenization. Our method produces realistic animations of knitwear matching the quality of full-scale yarn-level simulations. It is also orders of magnitude faster than existing homogenization techniques in both the training and simulation stages.

cs.GR↗

arXiv2024

Embedded IPC: Fast and Intersection-free Simulation in Reduced Subspace for Robot Manipulation

Physics-based simulation is essential for developing and evaluating robot manipulation policies, particularly in scenarios involving deformable objects and complex contact interactions. However, existing simulators often struggle to balance computational efficiency with numerical accuracy, especially when modeling deformable materials with frictional contact constraints. We introduce an efficient subspace representation for the Incremental Potential Contact (IPC) method, leveraging model reduction to decrease the number of degrees of freedom. Our approach decouples simulation complexity from the resolution of the input model by representing elasticity in a low-resolution subspace while maintaining collision constraints on an embedded high-resolution surface. Our barrier formulation ensures intersection-free trajectories and configurations regardless of material stiffness, time step size, or contact severity. We validate our simulator through quantitative experiments with a soft bubble gripper grasping and qualitative demonstrations of placing a plate on a dish rack. The results demonstrate our simulator's efficiency, physical accuracy, computational stability, and robust handling of frictional contact, making it well-suited for generating demonstration data and evaluating downstream robot training applications.

cs.RO↗

arXiv2024

XPBI: Position-Based Dynamics with Smoothing Kernels Handles Continuum Inelasticity

PBD and its extension, XPBD, have been predominantly applied to compliant constrained elastodynamics, with their potential in finite strain (visco-) elastoplasticity remaining underexplored. XPBD is often perceived to stand in contrast to other meshless methods, such as the MPM. MPM is based on discretizing the weak form of governing partial differential equations within a continuum domain, coupled with a hybrid Lagrangian-Eulerian method for tracking deformation gradients. In contrast, XPBD formulates specific constraints, whether hard or compliant, to positional degrees of freedom. We revisit this perception by investigating the potential of XPBD in handling inelastic materials that are described with classical continuum mechanics-based yield surfaces and elastoplastic flow rules. Our inspiration is that a robust estimation of the velocity gradient is a sufficiently useful key to effectively tracking deformation gradients in XPBD simulations. By further incorporating implicit inelastic constitutive relationships, we introduce a plasticity in-the-loop updated Lagrangian augmentation to XPBD. This enhancement enables the simulation of elastoplastic, viscoplastic, and granular substances following their standard constitutive laws. We demonstrate the effectiveness of our method through high-resolution and real-time simulations of diverse materials such as snow, sand, and plasticine, and its integration with standard XPBD simulations of cloth and water.

cs.GR↗

arXiv2024

Calibrating Noise for Group Privacy in Subsampled Mechanisms

Given a group size m and a sensitive dataset D, group privacy (GP) releases information about D with the guarantee that the adversary cannot infer with high confidence whether the underlying data is D or a neighboring dataset D' that differs from D by m records. GP generalizes the well-established notion of differential privacy (DP) for protecting individuals' privacy; in particular, when m=1, GP reduces to DP. Compared to DP, GP is capable of protecting the sensitive aggregate information of a group of up to m individuals, e.g., the average annual income among members of a yacht club. Despite its longstanding presence in the research literature and its promising applications, GP is often treated as an afterthought, with most approaches first developing a DP mechanism and then using a generic conversion to adapt it for GP, treating the DP solution as a black box. As we point out in the paper, this methodology is suboptimal when the underlying DP solution involves subsampling, e.g., in the classic DP-SGD method for training deep learning models. In this case, the DP-to-GP conversion is overly pessimistic in its analysis, leading to low utility in the published results under GP. Motivated by this, we propose a novel analysis framework that provides tight privacy accounting for subsampled GP mechanisms. Instead of converting a black-box DP mechanism to GP, our solution carefully analyzes and utilizes the inherent randomness in subsampled mechanisms, leading to a substantially improved bound on the privacy loss with respect to GP. The proposed solution applies to a wide variety of foundational mechanisms with subsampling. Extensive experiments with real datasets demonstrate that compared to the baseline convert-from-blackbox-DP approach, our GP mechanisms achieve noise reductions of over an order of magnitude in several practical settings, including deep neural network training.

cs.CR↗

arXiv2024

Investigation on a quantum algorithm for linear differential equations

Ref.[BCOW17] introduced a pioneering quantum approach (coined BCOW algorithm) for solving linear differential equations with optimal error tolerance. Originally designed for a specific class of diagonalizable linear differential equations, the algorithm was extended by Krovi in [Kro23] to encompass broader classes, including non-diagonalizable and even singular matrices. Despite the common misconception, the original algorithm is indeed applicable to non-diagonalizable matrices, with diagonalisation primarily serving for theoretical analyses to establish bounds on condition number and solution error. By leveraging basic estimates from [Kro23], we derive bounds comparable to those outlined in the Krovi algorithm, thereby reinstating the advantages of the BCOW approach. Furthermore, we extend the BCOW algorithm to address time-dependent linear differential equations by transforming non-autonomous systems into higher-dimensional autonomous ones, a technique also applicable for the Krovi algorithm.

quant-ph↗

arXiv2024

DPIS: An Enhanced Mechanism for Differentially Private SGD with Importance Sampling

Nowadays, differential privacy (DP) has become a well-accepted standard for privacy protection, and deep neural networks (DNN) have been immensely successful in machine learning. The combination of these two techniques, i.e., deep learning with differential privacy, promises the privacy-preserving release of high-utility models trained with sensitive data such as medical records. A classic mechanism for this purpose is DP-SGD, which is a differentially private version of the stochastic gradient descent (SGD) optimizer commonly used for DNN training. Subsequent approaches have improved various aspects of the model training process, including noise decay schedule, model architecture, feature engineering, and hyperparameter tuning. However, the core mechanism for enforcing DP in the SGD optimizer remains unchanged ever since the original DP-SGD algorithm, which has increasingly become a fundamental barrier limiting the performance of DP-compliant machine learning solutions. Motivated by this, we propose DPIS, a novel mechanism for differentially private SGD training that can be used as a drop-in replacement of the core optimizer of DP-SGD, with consistent and significant accuracy gains over the latter. The main idea is to employ importance sampling (IS) in each SGD iteration for mini-batch selection, which reduces both sampling variance and the amount of random noise injected to the gradients that is required to satisfy DP. Integrating IS into the complex mathematical machinery of DP-SGD is highly non-trivial. DPIS addresses the challenge through novel mechanism designs, fine-grained privacy analysis, efficiency enhancements, and an adaptive gradient clipping optimization. Extensive experiments on four benchmark datasets, namely MNIST, FMNIST, CIFAR-10 and IMDb, demonstrate the superior effectiveness of DPIS over existing solutions for deep learning with differential privacy.

cs.CR↗

arXiv2024

Unstructured Moving Least Squares Material Point Methods: A Stable Kernel Approach With Continuous Gradient Reconstruction on General Unstructured Tessellations

The Material Point Method (MPM) is a hybrid Eulerian Lagrangian simulation technique for solid mechanics with significant deformation. Structured background grids are commonly employed in the standard MPM, but they may give rise to several accuracy problems in handling complex geometries. When using (2D) unstructured triangular or (3D) tetrahedral background elements, however, significant challenges arise (\eg, cell-crossing error). Substantial numerical errors develop due to the inherent $\mathcal{C}^0$ continuity property of the interpolation function, which causes discontinuous gradients across element boundaries. Prior efforts in constructing $\mathcal{C}^1$ continuous interpolation functions have either not been adapted for unstructured grids or have only been applied to 2D triangular meshes. In this study, an Unstructured Moving Least Squares MPM (UMLS-MPM) is introduced to accommodate 2D and 3D simplex tessellation. The central idea is to incorporate a diminishing function into the sample weights of the MLS kernel, ensuring an analytically continuous velocity gradient estimation. Numerical analyses confirm the method's capability in mitigating cell crossing inaccuracies and realizing expected convergence.

cs.CE↗

arXiv2024

Gaussian Splashing: Unified Particles for Versatile Motion Synthesis and Rendering

We demonstrate the feasibility of integrating physics-based animations of solids and fluids with 3D Gaussian Splatting (3DGS) to create novel effects in virtual scenes reconstructed using 3DGS. Leveraging the coherence of the Gaussian Splatting and Position-Based Dynamics (PBD) in the underlying representation, we manage rendering, view synthesis, and the dynamics of solids and fluids in a cohesive manner. Similar to GaussianShader, we enhance each Gaussian kernel with an added normal, aligning the kernel's orientation with the surface normal to refine the PBD simulation. This approach effectively eliminates spiky noises that arise from rotational deformation in solids. It also allows us to integrate physically based rendering to augment the dynamic surface reflections on fluids. Consequently, our framework is capable of realistically reproducing surface highlights on dynamic fluids and facilitating interactions between scene objects and fluids from new views. For more information, please visit our project page at \url{https://gaussiansplashing.github.io/}.

cs.GR↗

arXiv2024

Skellam Mixture Mechanism: a Novel Approach to Federated Learning with Differential Privacy

Deep neural networks have strong capabilities of memorizing the underlying training data, which can be a serious privacy concern. An effective solution to this problem is to train models with differential privacy, which provides rigorous privacy guarantees by injecting random noise to the gradients. This paper focuses on the scenario where sensitive data are distributed among multiple participants, who jointly train a model through federated learning (FL), using both secure multiparty computation (MPC) to ensure the confidentiality of each gradient update, and differential privacy to avoid data leakage in the resulting model. A major challenge in this setting is that common mechanisms for enforcing DP in deep learning, which inject real-valued noise, are fundamentally incompatible with MPC, which exchanges finite-field integers among the participants. Consequently, most existing DP mechanisms require rather high noise levels, leading to poor model utility. Motivated by this, we propose Skellam mixture mechanism (SMM), an approach to enforce DP on models built via FL. Compared to existing methods, SMM eliminates the assumption that the input gradients must be integer-valued, and, thus, reduces the amount of noise injected to preserve DP. Further, SMM allows tight privacy accounting due to the nice composition and sub-sampling properties of the Skellam distribution, which are key to accurate deep learning with DP. The theoretical analysis of SMM is highly non-trivial, especially considering (i) the complicated math of differentially private deep learning in general and (ii) the fact that the mixture of two Skellam distributions is rather complex, and to our knowledge, has not been studied in the DP literature. Extensive experiments on various practical settings demonstrate that SMM consistently and significantly outperforms existing solutions in terms of the utility of the resulting model.

cs.LG↗

arXiv2024

Barrier-Augmented Lagrangian for GPU-based Elastodynamic Contact

We propose a GPU-based iterative method for accelerated elastodynamic simulation with the log-barrier-based contact model. While Newton's method is a conventional choice for solving the interior-point system, the presence of ill-conditioned log barriers often necessitates a direct solution at each linearized substep and costs substantial storage and computational overhead. Moreover, constraint sets that vary in each iteration present additional challenges in algorithm convergence. Our method employs a novel barrier-augmented Lagrangian method to improve system conditioning and solver efficiency by adaptively updating an augmentation constraint sets. This enables the utilization of a scalable, inexact Newton-PCG solver with sparse GPU storage, eliminating the need for direct factorization. We further enhance PCG convergence speed with a domain-decomposed warm start strategy based on an eigenvalue spectrum approximated through our in-time assembly. Demonstrating significant scalability improvements, our method makes simulations previously impractical on 128 GB of CPU memory feasible with only 8 GB of GPU memory and orders-of-magnitude faster. Additionally, our method adeptly handles stiff problems, surpassing the capabilities of existing GPU-based interior-point methods. Our results, validated across various complex collision scenarios involving intricate geometries and large deformations, highlight the exceptional performance of our approach.

cs.DC↗

arXiv2024

Vertex Block Descent

We introduce vertex block descent, a block coordinate descent solution for the variational form of implicit Euler through vertex-level Gauss-Seidel iterations. It operates with local vertex position updates that achieve reductions in global variational energy with maximized parallelism. This forms a physics solver that can achieve numerical convergence with unconditional stability and exceptional computation performance. It can also fit in a given computation budget by simply limiting the iteration count while maintaining its stability and superior convergence rate. We present and evaluate our method in the context of elastic body dynamics, providing details of all essential components and showing that it outperforms alternative techniques. In addition, we discuss and show examples of how our method can be used for other simulation systems, including particle-based simulations and rigid bodies.

cs.GR↗